4.5 COMPOSITE STEEL AND CONCRETE
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1 4.5 COMPOSITE STEEL AND CONCRETE RULES OF THUMB 4.5 Composite Steel and Concrete (1/11) Typical starting point Overall concrete depth 130mm (Grade 30) Depth of profiled decking 60mm Size beam with Z = ( Z for non-composite beam ) x F where F = Typical maximum slab spans (m) 1 Figures based on: "Ribdeck AL" (Richard Lees Ltd) Imposed load of 4+1 kn/m 2 (unfactored) (including floor, ceiling and services = 6.7 kn/m 2 ) Unpropped For other profiles see section D2 Decking gauge Slab depth (mm) Lightweight concrete Simply Supported Continuous Normal Concrete Simply Supported Continuous 0.9 (A142 mesh) (A193 mesh) Design assumes 60 minute fire resistance, provided that the slab is continious (decking need not be) Choice of beam system Likely span range (m) Economic and practical maximum Accommodation of major services. Scheme As primary As secondary ratios of span to structural depth Maximum x- sectional area for 15m span m² Simple construction with rolled sections - Fabricated Above 12 Above 12 sections Haunched 25 (support) 5.3 Above 12 Above 12 32(midspan) 3.6 Parallel Beam Spans up 21 approach Ribs up to to Castellated N/A up to 16 sections Stub girders N/A Composite Above 12 Above 12 trusses Slimfloor to Slimdek - 5 to Estimated unit cost index for fabricated and erected steelwork with reinforced openings
2 4.5 Composite Steel and Concrete (2/11) RULES OF THUMB (CONT D) Preferred beam layout 2 Inefficient Efficient For maximum structural efficiency: L secondary L primary = 4 / m spacing Initial scheming chart Universal, 125mm concrete slab (Dotted Line on upper graph indicates that a 150mm slab may be required).
3 4.5 Composite Steel and Concrete (3/11) RULES OF THUMB (CONT D) Fabricated Castellated cellular (not very good for point loads): Span/depth < 20 Castellated, hole = 0.67D centres = 0.72D Cellular holes diameter = 0.6D - 0.8D centres = diameter Haunched (use as part of frame action): D = midspan depth Span/depth 35 (span/depth including slab = 26 28) Maximum overall depth at haunch = 2D Haunch length typically 7-10% of span Tapered : D = midspan depth Span/depth Depth at support = 0.5D or maximum taper of 6 degrees Openings in (non-seismic applications) Geometrical constraints : - Limit unstiffened openings to 0.6D depth by 1.5D length - Limit stiffened openings to 0.7D depth by 2D length - Space > D apart - Ideally positioned between L/5 and L/3 from support for with UDL - Position > D from any point load - Position > 2D (or L/10) from support - Openings should ideally be located mid-height. If not, the depths of the upper and lower sections of web should not differ by more than a factor of 2.
4 4.5 Composite Steel and Concrete (4/11) LOAD FACTORS As for non-composite steel (see section 4.4.2) BENDING RESISTANCE (composite condition) 3 Approximate moment resistance calculation P.N.A. 0.45f cu y P P.N.A. R c y p D - D s p P.N.A. R c y p Py R C D P y y p IN SLAB y p IN STEEL FLANGE IN STEEL WEB y p Case (c) Case (b) Case(c)
5 4.5 Composite Steel and Concrete (5/11) Bending Resistance Formulae (Assuming 100% interaction) R s = p y A R c = 0.45 f cu (D s - D p )B e B e = 0.25 L beam spacing CASE (a) : R c > R s (P.N.A. in concrete slab) D Rs Ds - Dp Mpc = Rs + Ds - 2 Rc 2 CASE (b) : R s > R c > R w (P.N.A. in steel flange) 2 D Ds + Dp (Rs - Rc ) T Mpc = Rs + Rc Rf 4 where T = flange thickness R f = axial capacity of one steel flange CASE (c) : R c < R w (P.N.A. lies in web) 2 Ds + Dp + D Rc D Mpc = Ms +Rc - 2 Rw 4 where M s = plastic capacity of steel section R w = axial resistance of web only SHEAR CONNECTORS 4 Design strength of headed studs in normal weight concrete (kn) Dimensions of stud shear connectors (mm) Design strength of concrete (N/mm²) Diameter Nominal height As-welded height For concrete of characteristic strength greater than 40 N/mm² use the values for 40 N/mm². For connectors of heights greater than tabulated use the values for the greatest height tabulated. r con = 0.9 for lightweight concrete N = no studs/trough = 1.0 for normal weight concrete h = stud height r profile 0.85 b a = average trough width ba (h- D p) = min 0.8 (N = 2 ) D p = depth profile N Dp Dp min 0.6 (N = 3 ) Design resistance = Design strength x r con x r profile Spacing Minimum longitudinal = 6φ Maximum longitudinal = 600mm transverse = 4φ
6 4.5 Composite Steel and Concrete (6/11) BENDING STRENGTH (DURING CONSTRUCTION) Conform with requirements in section 4.4 for non-composite sections. Decking perpendicular to beam (secondary) provides restraint to top flange. Decking parallel to beam (primary) does not provide restraint STIFFNESS 3 Approximate ratio of second moment of area of composite section to that of the steel section. α = 10 α = 15
7 4.5 Composite Steel and Concrete (7/11) SAFE LOAD TABLES Concrete grade C35 Modular ratio 15 Overall concrete depth Depth of decking 130 mm 60 mm Partial interaction 60% Flange width as large as possible Deflection limit DL : 1/200 LL : 1/350 Dead Load steelwork - self weight decking kpa slab (dense) kpa slab (lightweight) kpa services + ceiling kpa REFERENCES 1. RICHARD LEES Ltd, Steel Deck Flooring Systems 2. STEEL CONSTRUCTION INSTITUTE, Steel Designers Manual 3. STEEL CONSTRUCTION INSTITUTE, SCI-P-055 Design of Composite Slabs and with Steel Decking 4. BS 5950 Structural use of steelwork in building Part 3: Design in composite construction
8 4.5 Composite Steel and Concrete (8/11) SAFE LOAD TABLES (1) GRADE 43 - DENSE CONCRETE SLAB Imposed load = kn/m 2 Minimum Minimum Depth Bay size (m x m) No. sec. per grid Spacing of sec. ( kg/m 2 ) 60x x 102 x x 140 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 140 x x 152 x x 203 x x 254 x x x 152 x x 191 x x 254 x x 254 x x x 152 x x 210 x x 254 x x 254 x x x 210 x x 210 x x 254 x 167* 305 x 305 x x x 229 x 113 * 610 x 229 x x 305 x 240* 305 x 305 x x x 267 x 147 * 610 x 229 x x 406 x 340* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 171 x x 210 x x 203 x x 254 x x x 152 x x 229 x x 254 x132* 305 x 305 x x x 254 x 125 * 762 x 267 x x 406 x 287* 356 x 406 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 210 x x 203 x x 254 x x x 171 x x 210 x x 203 x x 305 x x x 152 x x 229 x x 254 x132* 305 x 305 x x x 229 x x 254 x x 305 x 198* 305 x 305 x x x 254 x 140 * 762 x 267 x x 406 x 287* 356 x 406 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 210 x x 203 x x 305 x x x 140 x x 229 x x 203 x x 305 x x x 152 x x 229 x x 254 x x 305 x x x 191 x x 229 x x 254 x132* 305 x 305 x x x 229 x x 267 x x 305 x 198* 356 x 406 x x x 254 x 140 * 762 x 267 x x 406 x 287* 356 x 406 x x x 102 x x 210 x x 203 x x 254x x x 127 x x 229 x x 203 x x 305 x x x 127 x x 229 x x 203 x x 305 x x x 140 x x 229 x x 203 x x 305 x x x 152 x x 229 x x 254 x x 305 x x x 152 x x 229 x x 254 x x 305 x x x 210 x x 254 x x 254 x 167* 356 x 406 x x x 229 x 113 * 762 x 267 x x 305 x 240* 356 x 406 x x x 267 x 147 * 838 x 292 x x 406 x 340* COLCORE x x x 102 x x 229 x x 203 x x 305 x x x 127 x x 254 x x 203 x x 406 x x x 171 x x 267 x x 203 x x 406 x x x 152 x x 267 x x 254 x x 406 x x x 152 x x 292 x x 254 x 132* 356 x 406 x x x 229 x x 305 x x 305 x 198* 356 x 406 x x x 254 x 140 * 914 x 305 x x 406 x 287* 356 x 406 x x x 102 x x 254 x x 203 x x 406 x x x 127 x x 254 x x 203 x x 406 x x x 127 x x 267 x x 203 x x 406 x x x 140 x x 267 x x 203 x x 406 x x x 152 x x 292 x x 254 x 89 COLCORE x x x 152 x x 305 x x 254 x x 406 x x x 210 x x 305 x x 254 x 167* 356 x 406 x x x 229 x 113 * 914 x 305 x x 305 x 240* 914 x 419 x x x 267 x 147 * 914 x 419 x x 406 x 340* 914 x 419 x x x 102 x x 292 x x 203 x 46 COLCORE x 477* x x 127 x x 305 x x 203 x x 406 x x x 140 x x 305 x x 203 x x 406 x x x 152 x x 305 x x 254 x x 406 x 634* x x 152 x x 305 x x 254 x x 305 x 289* x x 210 x x 419 x 343 * x 254 x 167* 914 x 419 x 388* x x 229 x 113 * FAIL 305 x 305 x 240* FAIL 15.0 x x 267 x 147 * FAI L 356 x 406 x 340* FAIL 18.0 x x 102 x x 305 x 253 * x 203 x x 406 x 634* x x 127 x x 419 x 343 * x 203 x x 419 x 343* x x 127 x x 419 x 343 * x 203 x x 419 x 343* x x 140 x x 419 x 343 * x 203 x x 419 x 388* x x 152 x 52 FAIL 254 x 254 x 89 FAIL 18.0 x x 152 x 60 FAIL 254 x 254 x 107 FAIL 18.0 x x 210 x 82 FAIL 254 x 254 x 167* FAIL 18.0 x x 229 x 113 * FAIL 305 x 305 x 240* FAIL 18.0 x x 267 x 347 * FAIL 356 x 406 x 340* FAIL (*) Natural frequency of the beam is less then 4.5Hz.
9 4.5 Composite Steel and Concrete (9/11) SAFE LOAD TABLES (2) GRADE 43 - LIGHTWEIGHT CONCRETE SLAB Imposed load = kn/m 2 Minimum Minimum Depth Bay size (m x m) No. sec. per grid Spacing of sec. 6.0 x x 102 x x 140 x x 203 x x 203 x x x 127 x x 152 x x 203 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 140 x x 152 x x 203 x x 254 x x x 152 x x 191 x x 254 x x 254 x x x 191 x x 210 x x 254 x x 254 x x x 229 x x 229 x x 305 x 198* 305 x 305 x x x 254 x 140* 610 x 229 x x 406 x 340* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 210 x x 203 x x 254 x x x 152 x x 229 x x 254 x x 305 x x x 229 x 125* 686 x 254 x x 406 x 287* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 191 x x 203 x x 254 x x x 140 x x 210 x x 203 x x 254 x x x 152 x x 229 x x 254 x x 305 x x x 210 x x 229 x x 305 x 198* 305 x 305 x x x 229 x 125* 762 x 267 x x 406 x 287* 356 x 406 x x x 102 x x 152 x x 152 x x 254 x x x 127 x x 210 x x 203 x x 254 x x x 140 x x 210 x x 203 x x 305 x x x 152 x x 229 x x 254 x x 305 x x x 152 x x 229 x x 254 x x 305 x x x 229 x x 254 x x 305 x 198* 356 x 406 x x x 254 x 125* 686 x 254 x x 406 x 287* 356 x 406 x x x 102 x x 210 x x 203 x x 254 x x x 127 x x 210 x x 203 x x 305 x x x 102 x x 210 x x 203 x x 305 x x x 127 x x 229 x x 203 x x 305 x x x 140 x x 229 x x 203 x x 305 x x x 152 x x 229 x x 254 x x 305 x x x 191 x x 254 x x 254 x x 406 x x x 229 x x 254 x x 305 x 198* 356 x 406 x x x 254 x 140* 838 x 292 x x 406 x 340* COLCORE x x x 102 x x 229 x x 152 x x 305 x x x 127 x x 229 x x 203 x x 305 x x x 140 x x 254 x x 203 x x 406 x x x 140 x x 267 x x 203 x x 406 x x x 152 x x 267 x x 254 x x 406 x x x 210 x x 305 x x 305 x 198* 356 x 406 x x x 229 x 125* 914 x 305 x x 406 x 287* 356 x 406 x x x 102 x x 254 x x 203 x x 305 x x x 127 x x 267 x x 203 x x 406 x x x 102 x x 267 x x 203 x x 406 x x x 127 x x 267 x x 203 x x 406 x x x 140 x x 292 x x 203 x x 406 x x x 152 x x 292 x x 254 x 107 COLCORE x x x 191 x x 305 x x 254 x x 406 x x x 229 x x 305 x x 305 x 198* 356 x 406 x x x 254 x 140* 914 x 419 x x 406 x 340* 914 x 419 x x x 102 x x 267 x x 203 x x 406 x 393* x x 102 x x 305 x x 203 x x 406 x x x 127 x x 305 x x 203 x x 406 x x x 140 x x 305 x x 203 x x 406 x 634* x x 152 x x 305 x x 254 x x 406 x 634* x x 191 x x 419 x x 254 x x 419 x x x 229 x 101 FAIL 305 x 305 x 198* FAIL 15.0 x x 254 x 140* FAIL 356 x 406 x 340* FAIL 18.0 x x 102 x x 305 x 253 * x 203 x x 406 x 634* x x 127 x x 305 x 289 * x 203 x x 305 x 289* x x 102 x x 419 x 343 * x 203 x x 419 x 343* x x 127 x x 419 x 343* x 203 x x 419 x 34 * x x 140 x x 419 x 388* x 203 x x 419 x 388* x x 152 x 52 FAIL 254 x 254 x 107 FAIL 18.0 x x 191 x 74 FAIL 254 x 254 x 167 FAIL 18.0 x x 229 x 101 FAIL 305 x 305 x 198* FAIL 18.0 x x 254 x140* FAIL 356 x 406 x 340* FAIL (*) Natural frequency of the beam is less then 4.5Hz. AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY. Ver 3.1 / August 00
10 4.5 Composite Steel and Concrete (10/11) SAFE LOAD TABLES (3) GRADE 50 - DENSE CONCRETE SLAB Imposed load = kn/m 2 Minimum Minimum Depth Bay size (m x m) No. sec. per grid Spacing of sec. 6.0 x x 102 x x 140 x x 152 x x 203 x x x 102 x x 140 x x 203 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 140 x x 152 x x 203 x x 254 x x x 152 x x 152 x x 254 x x 254 x x x 191 x x 210 x x 254 x132* 254 x 254 x x x 210 x x 210 x x 305 x 198* 305 x 305 x x x 254 x x 229 x x 406 x 340* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 152 x x 210 x x 254 x 107* 254 x 254 x x x 229 x x 229 x x 406 x 287* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 152 x x 210 x x 254 x 107* 305 x 305 x x x 210 x x 229 x x 305 x 198* 305 x 305 x x x 229 x 113 * 686 x 254 x x 406 x 287* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 210 x x 203 x x 254 x x x 140 x x 210 x x 203 x x 305 x x x 152 x x 229 x x 254 x 132* 305 x 305 x x x 210 x x 229 x x 305 x 198* 305 x 305 x x x 229 x 125* 762 x 267 x x 406 x 287* 356 x 406 x x x 102 x x 191 x x 152 x x 254 x x x 102 x x 210 x x 203 x x 254 x x x 102 x x 210 x x 203 x x 254 x 167* x x 127 x x 210 x x 203 x x 305 x x x 140 x x 229 x x 203 x x 305 x x x 152 x x 229 x x 254 x x 305 x x x 152 x x 229 x x 254 x 132* 305 x 305 x 240* x x 210 x x 267 x x 305 x 198* 356 x 406 x 287* x x 254 x 125* 762 x 267 x x 406 x 340* 356 x 406 x 340* x x 102 x x 210 x x 152 x x 305 x 158* x x 102 x x 229 x x 203 x x 305 x 240* x x 127 x x 229 x x 203 x x 305 x 240* x x 140 x x 254 x x 203 x x 305 x 283* x x 152 x x 267 x x 254 x 107* 3% x 406 x 340* x x 210 x x 292 x x 305 x 198* 356 x 406 x 393* x x 229 x x 305 x x 406 x 287* COLCORE x 477* x x 102 x x 229 x x 152 x x 305 x 240* x x 102 x x 254 x x 203 x x 305 x 283* x x 102 x x 254 x x 203 x x 305 x x x 127 x x 267 x x 203 x x 406 x 287* x x 140 x x 254 x x 203 x x 406 x 340* x x 152 x x 267 x x 254 x x 406 x 340* x x 152 x x 292 x x 254 x 332* COLCORE x 477* x x 210 x x 305 x x 305 x198* 356 x 406 x x x 254 x x 305 x x 406 x 340* 914 x 419 x x x 102 x x 267 x 147 * x 152 x x 406 x 393* x x 102 x x 292 x 176 * x 203 x 52 COLCORE x 477* x x 127 x x 292 x 194 * x 203 x x 406 x 467* x x 140 x x 305 x 201 * x 203 x x 406 x x x 152 x x 305 x 224 * x 254 x x 406 x 634* x x 152 x x 305 x 289 * x 254 x132* 914 x 305 x 289* x x 210 x x 419 x 343 * x 305 x198* 914 x 419 x 343* x x 254 x 125 FAIL 356 x 406 x 340* FAIL 18.0 x x 102 x x 305 x 201 * x 152 x x 406 x 634 * x x 102 x x 305 x 253 * x 203 x x 305 x 253* x x 102 x x 305 x 253 * x 203 x x 305 x 253* x x 127 x x 305 x 289 * x 203 x x 305 x 289* x x 140 x x 419 x 343 * x 203 x x 419 x 343* x x 152 x x 419 x 343 * x 254 x x 419 x 343* x x 152 x 67 FAIL 254 x 254 x 132* FAIL 18.0 x x 210 x 92 FAIL 305 x 305 x 198* FAIL 18.0 x x 254 x 125 FAIL 356 x 406 x 340* FAIL (*) Natural frequency of the beam is less then 4.5Hz. AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY. Ver 3.1 / August 00
11 4.5 Composite Steel and Concrete (11/11) SAFE LOAD TABLES (4) GRADE 50 - LIGHTWEIGHT CONCRETE SLAB Imposed load = kn/m 2 Minimum Minimum Depth Bay size (m x m) No. sec. per grid Spacing of sec. 6.0 x x 102 x x 127 x x 152 x x 203 x x x 102 x x 140 x x 203 x x 203 x x x 102 x x 140 x x 203 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 140 x x 191 x x 254 x x 254 x x x 191 x x 191 x x 254 x132* 254 x 254 x x x 210 x x 210 x x 305 x 198* 254 x 254 x x x 229 x 125* 610 x 229 x x 406 x 340* 305 x 305 x x x 102 x x 140 x x 152 x x 254 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 152 x x 210 x x 254 x 107* 254 x 254 x x x 229 x x 229 x x 406 x 287* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x B3 7.5 x x 102 x x 152 x x 203 x x 254 x x x 127 x x 152 x x 203 x x 254 x x x 152 x x 210 x x 254 x132* 305 x 305 x x x 210 x x 229 x x 305 x 198* 305 x 305 x x x 229 x x 229 x x 406 x 287* 305 x 305 x x x 102 x x 152 x x 152 x x 254 x x x 102 x x 152 x x 203 x x 254 x x x 127 x x 210 x x 203 x x 254 x x x 140 x x 210 x x 203 x x 254 x x x 152 x 52* 610 x 229 x x 254 x132* 305 x 305 x x x 210 x 82* 610 x 229 x x 305 x198* 305 x 305 x x x 229 x 101* 686 x 254 x x 406 x 287* 305 x 305 x x x 102 x x 191 x x 152 x x 254 x x x 102 x x 210 x x 203 x x 254 x x x 102 x x 210 x x 203 x x 254 x x x 102 x x 210 x x 203 x x 254 x x x 127 x x 210 x x 203 x x 305 x x x 140 x x 229 x x 254 x x 305 x x x 152 x x 229 x x 254 x132* 305 x 305 x 240 ' x x 210 x x 254 x x 305 x198* 305 x 305 x x x 229 x x 254 x x 406 x 340* 356 x 406 x x x 102 x x 210 x x 152 x x 254 x 167* x x 102 x x 229 x x 203 x x 305 x 198* x x 127 x x 229 x x 203 x x 305 x x x 127 x x 254 x x 203 x x 305 x x x 152 x x 267 x x 254 x 107* 356 x 406 x 287* x x 210 x x 267 x x 305 x 198* 356 x 406 x x x 229 x x 292 x x 406 x 287* COLCORE x 477* x x 102 x x 229 x x 152 x x 305 x 240* x x 102 x x 254 x x 203 x x 305 x 283* x x 102 x x 254 x x 203 x x 305 x 283* x x 102 x x 254 x x 203 x x 406 x 287* x x 127 x x 267 x x 203 x x 406 x x x 140 x x 254 x x 254 x x 406 x 340* x x 152 x x 292 x x 254 x132* 356 x 406 x 393* x x 210 x x 305 x x 305 x198* 356 x 406 x x x 229 x x 305 x x 406 x 340* 356 x 406 x 634* x x 102 x x 267 x 147* x 152 x x 406 x 393* x x 102 x x 267 x 173* x 203 x 46 COLCORE x 477* x x 102 x x 292 x 176* x 203 x x 406 x 467* x x 127 x x 292 x 194* x 203 x x 406 x x x 140 x x 305 x 224* x 254 x x 406 x 634* x x 152 x x 305 x 253* x 254 x 132* 914 x 305 x x x 210 x 82* 914 x 419 x 343* x 305 x 198* 914 x 419 x 343* x x 229 x 125* 914 x 419 x 388* x 406 x 340* 914 x 419 x 388* x x 102 x x 292 x 194* x 152 x x 406 x 634* x x 102 x x 305 x 224* x 203 x x 305 x 224* x x 102 x x 305 x 253* x 203 x x 305 x 253* x x 102 x x 305 x 253* x 203 x x 305 x 253* x x 127 x x 305 x 289* x 203 x x 305 x 289* 55.7B 18.0 x x 340 x x 419 x 343* x 254 x x 419 x 343* x x 152 x x 419 x 388* x 254 x132* 914 x 419 x 388* x x 210 x 82 FAIL 305 x 305 x 198* FAIL 18.0 x x 229 x 125 FAIL 356 x 406 x 340* FAIL (*) Natural frequency of the beam is less then 4.5Hz. AND SHOULD NOT BE RELIED UPON BY ANY THIRD PARTY. Ver 3.1 / August 00
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